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Tuesday, January 3, 2012

A More Auspicious Beginning to Surface Area and Volume

For a few years, by the time December rolls around, I am so beat up by daily grading, making copies, paperwork, being a good example for the youth of America, etc etc, that my Surface Area/Volume unit has always been just fantastically awful. Although it's been a long December, I was determined to make this at least a little better.

I start with surface areas, because we just spent tons of time working with areas of composite figures and shaded regions, so it makes sense to extend that.

So to start out, instead of this (try not to barf:)

I sneakily ask them to calculate some composite areas.
I am not super-thrilled with these. In the future I would make them bigger and use more integral values, and not use such a tall, skinny cone.

As they were working, I asked them to write how they calculated the area in the middle of the shape. So in that last one they might write "Area = 1 rectangle and 2 circles."

The cylinder was VERY interesting, since there's really nothing given about the height of the rectangle, but by now they tend to assume that if they need a dimension, there should be a way to figure it out. Some kids realized we were going to turn it into a cylinder and used the circumference of the circles, but some kids estimated that the height of the rectangle was about three circles, which I didn't anticipate but hey, pi is about 3, and that's kind of awesome.

Anyway, so now we are going to cut these out and hold on to them for a few days.

Hopefully avoiding the phenomenon of having no idea which dimensions we need or randomly plugging given numbers into given formulas.

I don't really know where we're going to go from here. I might freak out and go back to a traditional approach, but at least more kids might have a better idea of what those formulas are all about.


  1. Random idea that might be terrible or might be awesome.

    My sister and I started making Santa presents for our parents years ago. Mine are usually made last minute and are grade-school craft type things.

    This year I was inspired by this to make Christmas ornaments out of the cereal boxes in the recycling bin. So there's a cheerios ornament, a raisin bran ornament, and a grapenuts ornament.

    Only after I traced the patten for all of them did I realize that I should have gone back to the geometry tools and used a variety of different prism patterns.

    I know there's no time. But if you've already got the kids cutting out the patterns, I wonder if it'd be possible to tape in the string, tape up the models, and decorate. Hang them from the ceiling for the week? Or the rest of the year? Would having the shapes hanging over the head help them remember where the different numbers belong?

  2. That is a good idea Sarah. I was going to use Mimi's composite figure project, but it would be cool to have stuff hanging in the room. I'll have to think on it.

  3. Link to Mimi's project because I almost didn't find it. And someone else might reference your blog for ideas sometime. :)

  4. How about filling them with sand for volume and using a scale to measure?

  5. Thank you for posting the old along with the new and being so honest about your work. I like the fact that your ideas are so practical, realistic, and clearly the type of thing you are trying in your classroom on a day to day basis.


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